Bài giảng Managerial Accounting - Chapter 5: Cost-Volume-Profit Relationships

John Wiley & Sons, Inc.Prepared byKarleen Nordquist..The College of St. Benedict... and St. John’s University...with contributions byMarianne Bradford..The University of Tennessee...Gregory K. Lowry.Macon Technical Institute..Managerial Accounting Weygandt, Kieso, & KimmelChapter 5Cost-Volume-Profit RelationshipsAfter studying this chapter, you should be able to:1 Distinguish between variable and fixed costs.2 Explain the meaning and importance of the relevant range.3 Explain the concept of mixed costs.4 State the five components of cost-volume-profit analysis.5 Indicate the meaning of contribution margin and the ways it may be expressed.Chapter 5Cost-Volume-Profit RelationshipsAfter studying this chapter, you should be able to:6 Identify the three ways that the break-even point may be determined.7 Define margin of safety and give the formulas for computing it.8 Give the formulas for determining sales required to earn target net income.9 Describe the essential features of a cost-volume-profit income statement.Chapter 5Cost-Volume-Profit RelationshipsPreview of Chapter 5Cost Behavior AnalysisVariable CostsFixed CostsRelevant RangeMixed CostsIdentifying Variable and Fixed CostsCOST-VOLUME-PROFIT RELATIONSHIPSPreview of Chapter 5Cost-Volume-Profit AnalysisBasic ComponentsContribution MarginBreak-Even AnalysisMargin of SafetyTarget Net IncomeChanges in Business EnvironmentCVP Income StatementCOST-VOLUME-PROFIT RELATIONSHIPSCost Behavior AnalysisCost behavior analysis is the study of how specific costs respond to changes in the level of activity within a company.The starting point in cost behavior analysis is measuring the key activities in the company’s business.Activity levels may be expressed in terms ofsales dollars (retail company),miles driven (trucking company),room occupancy (hotel), ornumber of dance classes taught (dance studio).Cost Behavior AnalysisFor an activity level to be useful in cost behavior analysis, there should be correlation between changes in the level or volume of activity and changes in the costs.The activity level selected is referred to as the activity (or volume) index.The activity index identifies the activity that causes changes in the behavior of costs. Distinguish between variable and fixed costs.Study Objective 1Variable CostsVariable costs are costs that vary in total directly and proportionately with changes in the activity level. A variable cost may also be defined as a cost that remains the same per unit at every level of activity.Variable CostsDamon Company manufactures radios that contain a $10 digital clock. The activity index is the number of radios produced. As each radio is manufactured, the total cost of the clocks increases by $10.$100806040200Cost (000)0246810Radios produced in (000)(a) Total Variable Costs (Digital Clocks)05$25201510Cost (per unit)0246810Radios produced in (000)(b) Unit Variable Costs (Digital Clocks)Illustration 5-1Fixed CostsFixed costs are costs that remain the same in total regardless of changes in the activity level. Since fixed costs remain constant in total as activity changes, fixed costs per unit vary inversely with activity. As volume increases, unit cost declines and vice versa.Fixed CostsDamon Company leases all of its productive facilities at a cost of $10,000 per month. Total fixed costs of the facilities will remain constant at every level of activity.Illustration 5-2$2520151050Cost (000)0246810Radios produced in (000)(a) Total Fixed Costs (Rent Expense)01 $5 432Cost (per unit)0246810Radios produced in (000)(b) Fixed Costs Per Unit (Rent Expense)Explain the meaning and importance of the relevant range.Study Objective 2Nonlinear Behavior of Variable and Fixed CostsIn the previous two slides, the assumption was made that total variable costs and total fixed costs were linear, and straight lines were used to represent both types of costs. A straight-line relationship does not usually exist for variable costs throughout the entire range of activity.In the real world, the relationship between variable cost behavior and changes in the activity level is often curvilinear, as shown in part (a) on the right. The behavior of total fixed costs through all levels of activity is shown in part (b).Cost ($)0(b)Total Fixed Costs Nonlinear20406080100Activity level (%)Cost ($)020406080100Activity level (%)(a) Total Variable Costs CurvilinearIllustration 5-3Linear Behavior Within Relevant Range Operating at zero or at 100% capacity is the exception for most companies. Companies usually operate over a narrower range – such as 40-80% of capacity. The relevant range of the activity index is the range over which a company expects to operate during a year.Within this range, as shown in both diagrams to the right, a straight-line relationship normally exists for both fixed and variable costs.Illustration 5-4Cost ($)0(b) Total Fixed Costs Nonlinear20406080100Activity level (%)Relevant RangeCost ($)020406080100Activity level (%)(a) Total Variable Costs CurvilinearRelevant RangeExplain the concept of mixed costs.Study Objective 3Mixed CostsMixed costs contain both a variable cost element and a fixed cost element.Sometimes called semivariable costs, mixed costs change in total but not proportionately with changes in the activity level.Behavior of a Mixed CostThe rental of a U-Haul truck is a good example of a mixed cost.Local rental terms for a U-Haul truck are $50 per day plus $.50 per mile. The per diem charge is a fixed cost with respect to miles driven, while the mileage charge is a variable cost. The graphic presentation of the rental cost for a one-day rental is shown on the right. 150$200 100 50Cost 0Total Cost LineVariable Cost ElementFixed Cost Element050100150200250300MilesIllustration 5-5Mixed Cost Classification for CVP AnalysisIn CVP analysis, it is assumed that mixed costs must be classified into their fixed and variable elements.Firms usually ascertain variable and fixed costs on an aggregate basis at the end of a time period, using the company’s past experience with the behavior of the mixed cost at various activity levels.The high-low method is a mathematical method that uses the total costs incurred at the high and low levels of activity.The High-Low MethodThe steps in calculating fixed and variable costs under this method are as follows:1 Determine variable cost per unit from the following formula:2 Determine the fixed cost by subtracting the total variable cost at either the high or the low activity level from the total cost at that activity level.Illustration 5-6Change inTotal CostsHigh minus Low Activity LevelVariable Costper Unit=The High-Low Method:Step 1To illustrate, assume that Metro Transit Company has the following maintenance costs and mileage data for its fleet of busses over a 4-month period:The high and low levels of activity are 50,000 miles in April and 20,000 miles in January. The difference in maintenance costs at these levels is $33,000 ($63,000-$30,000) and the difference in miles is 30,000 (50,000 - 20,000). Therefore, for Metro Transit, variable cost per unit is $1.10, computed as follows:$33,000  30,000 = $1.10MonthJanuaryFebruaryMiles Driven20,00040,000Total Cost$30,000$48,000MonthMarchAprilMiles Driven35,00050,000Total Cost$49,000$63,000Illustration 5-7The High-Low Method:Step 2Metro Transit Company would compute the fixed portion of its maintenance costs as shown below:Maintenance costs are therefore $8,000 per month plus $1.10 per mile. For example at 45,000 miles, estimated maintenance costs would be $49,500 variable (45,000 x $1.10), and $8,000 fixed. Illustration 5-8Total CostLess: Variable costs (50,000 x $1.10) (20,000 x $1.10)Total fixed costs High $63,000 55,000$ 8,000 Low $30,000 22,000$ 8,000Activity LevelThe High-Low MethodThe high-low method generally produces a reasonable estimate for analysis. However, it does not produce a precise measurement of the fixed and variable elements in a mixed cost because other activity levels are ignored in the computation.!State the five components of cost-volume-profit analysis.Study Objective 4Cost-Volume Profit AnalysisCost-volume-profit (CVP) analysis is the study of the effects of changes of costs and volume on a company’s profits.CVP analysis involves a consideration of the interrelationships among the following components:Volume or activity levelUnit selling priceVariable cost per unitTotal fixed costsSales mixCVP AssumptionsThe following assumptions underlie each CVP application: When these assumptions are not valid, the results of CVP analysis may be inaccurate.1 The behavior of both costs and revenues is linear throughout the relevant range of the activity index.2 All costs can be classified as either variable or fixed with reasonable accuracy.3 Changes in activity are the only factors that affect costs.4 All units produced are sold.5 When more than one type of product is sold, total sales will be in a constant sales mix. CVP AnalysisIn CVP analysis applications, the term cost includes manufacturing costs plus selling and administrative expenses.We will use Vargo Video Company as an example. Relevant data for the VCRs made by this company are as follows: Unit selling priceUnit variable costs Total monthly fixed costs$500$300$200,000Illustration 5-10Indicate the meaning of contribution margin and the ways it may be expressed.Study Objective 5Contribution MarginOne of the key relationships in CVP analysis is contribution margin (CM). Contribution margin is the amount of revenue remaining after deducting variable costs. The CM is then available to cover fixed costs and to contribute income for the company.For example, assume that Vargo Video sells 1,000 VCRs in one month, sales are $500,000 (1,000 x $500) and variable costs are $300,000 (1,000 x $300). Thus, contribution margin is $200,000, computed as follows:SalesVariable CostsContribution Margin-=$500,000$300,000$200,000-=Illustration 5-11Unit Contribution MarginViews differ as to the best way to express contribution margin (CM). Some favor a per unit basis. At Vargo Video, the contribution margin per unit is $200.Unit Selling PriceUnit Variable CostContribution Margin per Unit-=$500$300$200-=Illustration 5-12CM per unit indicates that for every VCR sold, Vargo Video will have $200 to cover fixed costs and contribute to income.Contribution Margin RatioOthers prefer to use a contribution margin ratio. At Vargo Video, the contribution margin ratio is 40%.Contribution Margin per UnitUnit Selling PriceContribution Margin Ratio=$200$50040%=Illustration 5-13The CM ratio means that 40 cents of each sales dollar ($1 x 40%) is available to apply to fixed costs and to contribute to income.Identify the three ways that the break-even point may be determined.Study Objective 6Break-Even AnalysisThe second key relationship in CVP analysis is the break-even point, which is the level of activity where total revenues equals total costs, both fixed and variable.Since no income is involved when the break-even point is the objective, the analysis is often referred to as break-even analysis.Break-Even AnalysisThe break-even point can be:Computed from a mathematical equation.Computed by using contribution margin.Derived from a CVP graph.The break-even point can be expressed in either sales dollars or sales units.Break-Even Analysis: Mathematical EquationIn its simplest form, the equation for break-even sales is:Break-even SalesVariable CostsFixed Costs=+Illustration 5-14Break-Even Analysis: Mathematical Equation for DollarsThe break-even point in dollars is found by expressing variable costs as a percentage of unit selling price. For Vargo Video, the percentage is 60% ($300  $500). Sales must be $500,000 for Vargo Video to break even. The computation to determine sales dollars at the break-even point is:Illustration 5-15 X = .60X + $200,000.40X = $200,000 X = $500,000where: X = sales dollars at the break-even point .60 = variable costs as a percentage of unit selling price $200,000 = total fixed costsBreak-Even Analysis: Mathematical Equation for UnitsThe break-even point in units can be computed directly from the mathematical equation by using unit selling prices and unit variable costs. Vargo must sell 1,000 units to break even. The computation is:Illustration 5-16$500X = $300X + $200,000$200X = $200,000 X = 1,000 unitswhere: X = sales volume $500 = unit selling price $300 = variable cost per unit $200,000 = total fixed costsBreak-Even Analysis: Mathematical Equation ProofThe accuracy of the previous computations can be proved as follows:Illustration 5-16$300,000 200,000Sales (1,000 x $500)Total costs: Variable (1,000 x $300) FixedNet Income$500,000 500,000$ -0- Break-Even Analysis:CM Technique for UnitsBecause we know that CM equals total revenues less variable costs, it follows that at the break-even point, contribution margin must equal total fixed costs. When the CM per unit is used, the formula to compute break-even point in units is shown below:Once again, the CM per unit for Vargo Video is $200.Fixed CostsContribution Margin per UnitBreak-even Point in Units=$200,000$2001,000=Break-Even Analysis:CM Technique for DollarsWhen the CM ratio is used, the formula to compute break-even point in dollars is shown below:Again, the CM ratio for Vargo Video is 40%.Fixed CostsContribution Margin RatioBreak-even Point in Dollars=$200,00040%$500,000=Break-Even Analysis:Graphic PresentationAn effective way to derive the break-even point is to prepare a break-even graph.The graph is referred to as a cost-volume-profit (CVP) graph since it shows costs, volume, and profits.Break-Even Analysis:Graphic PresentationThe construction of the graph, using the Vargo Video Company data, is as follows:1 Plot the total revenue line starting at the zero activity level.2 Plot the total fixed cost by a horizontal line.3 Plot the total cost line starting at the fixed cost line at zero activity and increasing the amount by the variable cost at each level of activity.4 Determine the break-even point from the intersection of the total cost line and the total revenue line. In addition to identifying the break-even point, the CVP graph shows both the net income and net loss areas. Thus, the amount of income or loss at each level of sales can be derived from the total sales and total cost lines.CVP GraphIn the graph to the right, sales volume is shown on the horizontal axis. This axis needs to extend to the maximum level of expected sales. Both total revenues (sales) and total costs (fixed plus variable) are recorded on the vertical axis.Dollars (000)Units of Sales$90070060050040030020010012002004006008001000140016001800Break-even PointProfit AreaSales LineTotal CostLineFixed CostLineLoss AreaIllustration 5-20Define margin of safety and give the formulas for computing it.Study Objective 7Margin of SafetyThe margin of safety is another relationship that may be calculated in CVP analysis. Margin of safety is the difference between actual or expected sales and sales at the break-even pointThis relationship measures the “breathing room” or “cushion” that management has in order to break even if actual sales fail to materialize.Margin of SafetyThe margin of safety may be expressed in dollars or as a ratio.Assuming that actual (expected) sales for Vargo Video are $750,000, the computations are:Actual (Expected) SalesBreak-even SalesMargin of Safety in Dollars-=$750,000$500,000$250,000-=Margin of Safety in DollarsMargin of Safety in DollarsActual (Expected) SalesMargin of Safety Ratio=$250,000$750,00033%=Margin of Safety RatioGive the formulas for determining sales required to earn target net income.Study Objective 8Target Net IncomeManagement usually sets an income objective for individual product lines. This objective, called target net income, is extremely useful to management because it indicates the sales necessary to achieve a specified level of income. The amount of sales necessary to achieve target net income can be determined from each of the approaches used in determining break-even sales.Target Net Income: Mathematical EquationWe know that at the break-even point no profit or loss results for the company. By adding a factor for target net income to the break-even equation, we obtain the formula shown below for determining required sales. Required sales may be expressed in either sales dollars or sales units.Illustration 5-23Required Sales=Variable Costs+Fixed Costs+Target Net IncomeTarget Net Income: Mathematical EquationAssuming the target net income is $120,000 for Vargo Video, the computation of required sales in dollars is as follows:Illustration 5-24 X = .60X + $200,000 + $120,000.40X = $320,000 X = $800,000where: X = required sales .60 = variable costs as a percentage of unit selling price $200,000 = total fixed costs $120,000 = target net incomeThe sales volume in units at the target income level is found by dividing the sales dollars by the unit selling price.$800,000  $500 = $1,600Target Net Income:CM TechniqueAs in the case of break-even sales, the sales required to meet a target net income can be computed in either dollars or units.The formula using the CM ratio for Video Vargo is as follows:Required SalesFixed Costs + Target Net IncomeContribution Margin Ratio$320,00040%$800,000==Target Net Income:Graphic PresentationA CVP graph can also be used to derive the sales required to meet target net income. In the profit area of the graph, the distance between the sales line and the total cost line at any point equals net income. Required sales are found by analyzing the differences between the two lines until the desired net income is found.CVP and Changes in the Business EnvironmentBusiness conditions change rapidly and management must respond intelligently to these changes.CVP analysis can be used in responding to change.The original VCR sales and cost data for Vargo Video Company are shown below.Unit selling price$ 500Unit variable cost$ 300Total fixed costs$ 200,000Break-even sales$ 500,000or 1,000 unitsIllustration 5-26Fixed Costs÷Contribution Margin per Unit=Break-even Sales$ 200,000÷$ 150=1,333 units (rounded)Illustration 5-27A competitor is offering a 10% discount on the selling price of its VCRs. Management must decide whether or not to offer a similar discount.Question: What effect will a 10% discount on selling price have on the break-even point for VCRs?Answer: A 10% discount on selling price reduces the selling price per unit to $450 [$500 – ($500 x 10%)]. Variable cost per unit remains unchanged at $300. Therefore, the contribution margin per unit is $150. Assuming no change in fixed costs, break-even sales are 1,333 units, calculated as follows: CVP and Changes in the Business Environment: Case IFixed Costs÷Contribution Margin per Unit=Break-even Sales$ 260,000÷($500 - $210)=900 units (rounded)Illustration 5-28Management invests in new robotic equipment that will significantly lower the amount of direct labor required to make the VCRs. It is estimated that total fixed costs will increase 30% and that variable cost per unit will decrease 30%.Question: What effect will the new equipment have on the sales volume required to break even?Answer: Total fixed costs become $260,000 [$200,000 + ($200,000 x 30%)], and variable cost per unit is now $210 [$300 – ($300,000 x 30%)]. The new break-even point about 900 units, calculated as follows: CVP and Changes in the Business Environment: Case IIAn increase in the price of raw materials will increase the unit variable cost of VCRs by an estimated $25. Management is striving to hold the line on the selling price of the VCRs, and plans a cost-cutting program that will save $17,500 in fixed costs per month. Vargo Video Company is currently realizing monthly net income of $80,000 on sales of 1,400 VCRs.Question: What increase in sales will be needed to to maintain the same level of net income?Answer: The variable cost per unit inc